Lectures related to Amalgams: Group Pushouts

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Categorical Perspective: Group Quotients

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Group Theory Basics: Subgroups and Homomorphisms

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Recap of Group Theory

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Universal Property of Groups

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Group Actions: Theory and Examples

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Classification of Extensions

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Group Direct Sums in Group Theory

Explores direct sums in group theory, focusing on abelian groups and their implications.

Push-out and Quotients

Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.

Topology: Free Groups and Their Properties

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Group Theory Basics

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Quotient Groups: Homomorphisms and Isomorphisms

Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.

Quotients de groupe: Un cas particulier

Explores a categorical perspective on group quotients, focusing on a specific case.

Two Definitions of Group Action

Explores two definitions of group action on a set, focusing on properties and applications.

Group Homomorphisms

Explores group homomorphisms, Euler's phi function, and group products.

First Isomorphism Theorem

Covers the first isomorphism theorem in group theory and its applications.

Group Theory: Special Cases

Covers special cases in group theory, focusing on group actions and functors.

Normal Subgroups and Quotients

Introduces normal subgroups, group quotients, and their applications in group theory.